1.7 Plane-wave Solutions of the Dirac Equation If ψ= eipxup, where px= pµxµ = p ·x −Et, the Dirac equation becomes (γp+m)up = 0. (1.172) For a particle at rest, p0 = m, p = 0, this is (1−γ0)v= 0, (1.173) where v= up=0 is the rest-frame spinor. This means that vis an eigenvector of γ0 with eigenvalue +1. Because [Σ3,γ 0] = 0, (1.174)